Kurz, nicknamed "wunderwuzzi" ("whizz-kid"), is now expected to enter coalition talks with the far-right Freedom Party (FPÖ), potentially giving the European Union a fresh headache.
Kurz's People's Party (ÖVP) came first in Sunday's election with 31.5 percent followed by the centre-left Social Democrats on 26.9 percent, final results showed late on Thursday.
The populist Freedom Party, highly critical of the EU, came a close third with 26.0 percent, just short of its 1999 record under former chief Jörg Haider of 26.9 percent.
Kurz said on Friday after being given a mandate by President Alexander Van der Bellen that he will now "sound out" all the other parties and then enter coalition negotiations.
"I want a new political culture, a new political style," he said. "I want a government that has the courage and the determination to bring about real change in Austria."